Auchincloss was born at Hammersmith Farm in Newport, Rhode Island. He was the son of Hugh Dudley Auchincloss, Sr. (1858–1913), a merchant and financier, and Emma Brewster Jennings, daughter of Oliver Burr Jennings and Esther Judson Goodsell. His uncles were Edgar Stirling Auchincloss (father of James C. Auchincloss) and John Winthrop Auchincloss (grandfather of Louis Auchincloss).[1][2] He had two older sisters, Esther Judson Auchincloss and Ann Burr Auchincloss. His father was the youngest brother of Edgar Stirling Auchincloss, making Hugh the nephew of Edgar Stirling Auchincloss and cousin of politician James C. Auchincloss.

Auchincloss had been a special agent with the Commerce Department before joining the State Department as an aviation specialist in 1927. Four years later, he resigned government service and used some of the enormous inheritance from his mother to found the Washington brokerage firm of Auchincloss, Parker & Redpath.

His first marriage, from June 4, 1925, to 1932, was to Maya de Chrapovitsky, a Russian noblewoman. They had one child, Hugh Dudley "Yusha" Auchincloss III (born 1927). His second marriage, from 1935 to 1941, was to Nina S. Gore (1903–1978), mother of author Gore Vidal. They had two children, Nina Gore Auchincloss (born 1935) and Thomas Gore Auchincloss (born 1937). On June 21, 1942, he married Janet Lee Bouvier, who was already mother of future First Lady Jacqueline Lee "Jackie" Bouvier and Caroline Lee Bouvier. They had two children, Janet Jennings Auchincloss (1945–1985) and James Lee Auchincloss (born 1947).

Auchincloss was responsible for getting Jacqueline Bouvier her first job in journalism at the Washington Times-Herald. He gave her away at her wedding to future president John F. Kennedy, the reception of which was held at Hammersmith Farm on September 12, 1953. A long-time financial contributor to the Republican Party, he contributed to the campaign of his Democratic stepson-in-law, saying "I want to live in harmony with Mrs. Auchincloss and all the other members of the family."